Finite Group Databasebeta

← #32981056

Subgroups — #32981056

Order 18688.

484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619016C211yesmaximal, characteristic
2#22613222C211yesmaximal, characteristic
3#22608379C212yesmaximal
4#22607825C212yesmaximal
5C4×#101×C73C211yesmaximal, characteristic
6C2×C4×Dic146C2211yescharacteristic
7#17988718—24no—
8#17988644—21no—
9#17988644C2212yes—
10#17988640—21no—
11#17988518—21no—
12#17988517C411yescharacteristic
13#17988517C411yescharacteristic
14#17988507C411yescharacteristic
15#17988507C411yescharacteristic
16#17988506—21no—
17C4×#11924007—21no—
18C4×#11924007—21no—
19#17988433C2211yescharacteristic
20#17988319—24no—
21C2×C4×Q8×C73C2211yescharacteristic
22C2×#101×C73—21no—
23C4×M16×C73C2212yes—
24#343×C73—21no—
25C22×Dic146C2×C411yescharacteristic
26C4×Dic146—22no—
27C4×Dic146—22no—
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×C4×Dic73—21no—
35C2×C4×Dic73—21no—
36C4⋊#10596831—22no—
37C4⋊#10596831—22no—
38C4⋊#10596831D414yes—
39C22⋊#10596831—22no—
40#14556502—22no—
41#14556502—22no—
42C4×#10596831—22no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498C2×C411yescharacteristic
49#14556498C2×C411yescharacteristic
50C22×Q8×C73D411yescharacteristic
51C2×M16×C73—22no—
52C4×Q8×C73—22no—
53C4×Q8×C73—22no—
54C2×C4⋊C4×C73C2×C411yescharacteristic
55C2×C4⋊C4×C73C2×C411yescharacteristic
56C2×C4⋊C4×C73D411yescharacteristic
57C2×C42×C73D411yescharacteristic
58C2×C42×C73D411yescharacteristic
59C2×C42×C73C2311yescharacteristic
60#101×C73—24no—
61#97×C73—22no—
62C4×C8×C73—22no—
63C2×Dic146—22no—
64C2×Dic146—42no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C2×#10596831—24no—
70C4⋊Dic73—22no—
71#11924007—42no—
72#11924007—42no—
73#11924007—42no—
74#11924007—42no—
75#11924007—42no—
76C4×Dic73—24no—
77C4×Dic73—41no—
78C4×Dic73—41no—
79C2×Q8×C73—22no—
80C2×Q8×C73—22no—
81C2×Q8×C73—41no—
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22⋊C411yescharacteristic
84C22×C4×C73C22⋊C411yescharacteristic
85C22×C4×C73C22⋊C411yescharacteristic
86C22×C4×C73C22×C411yescharacteristic
87C22×C4×C73C2×D411yescharacteristic
88C22×C4×C73C2×D411yescharacteristic
89M16×C73—24no—
90M16×C73—42no—
91C2×C8×C73—42no—
92C4⋊C4×C73—22no—
93C4⋊C4×C73—22no—
94C4⋊C4×C73—22no—
95C42×C73—21no—
96C42×C73—21no—
97C42×C73—21no—
98C42×C73—21no—
99C42×C73C2×D412yes—
100C42×C73#4112yes—
101C23×C73C2×C22⋊C411yescharacteristic
102Q8×C73—44no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—22no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73#10412yes—
117C2×C4×C73C4×D412yes—
118C2×C4×C73#12011yescharacteristic
119C2×C4×C73#12112yes—
120C2×C4×C73#12311yescharacteristic
121C2×Dic73—22no—
122C2×Dic73—22no—
123C2×Dic73—22no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133Dic146—24no—
134Dic146—42no—
135C8×C73—44no—
136#10596831—44no—
137C22×C73—21no—
138C22×C73—21no—
139C22×C73#38611yescharacteristic
140C22×C73C2×#10411yescharacteristic
141C22×C73#42111yescharacteristic
142C4×C73—22no—
143C4×C73—22no—
144C4×C73—21no—
145C4×C73—22no—
146C4×C73—41no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73#45612yes—
150Dic73—42no—
151Dic73—42no—
152Dic73—42no—
153Dic73—81no—
154#9030—731nomaximal, Sylow
155C2×C73—21no—
156C2×C73—21no—
157C2×C73#187111yescharacteristic
158C2×C73#188611yescharacteristic
159C2×C73#189111yescharacteristic
160#2983—731no—
161#2399—731no—
162C4×#101D7311yescharacteristic
163#1491—732no—
164#1300—732no—
165C73#903011yescharacteristic, complemented, Sylow
166C2×C4×Q8—731no—
167C2×C4×Q8C2×D7311yescharacteristic
168#446—1464no—
169#432—732no—
170#432—1461no—
171#431—1461no—
172C2×#101—21no—
173C4×M16C2×D7312yes—
174#398—731no—
175#398—731no—
176#398—1461no—
177#395—731no—
178#395—731no—
179#395—1461no—
180C4×C4⋊C4—1461no—
181C4×C4⋊C4—1461no—
182#376—731no—
183#343—21no—
184Q8⋊C8—1464no—
185C22×Q8—731no—
186C22×Q8C22⋊D7311yescharacteristic
187C2×M16—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—1462no—
191C4×Q8—1462no—
192C2×C4⋊C4—731no—
193C2×C4⋊C4—1461no—
194C2×C4⋊C4—1461no—
195C2×C4⋊C4—1461no—
196C2×C4⋊C4—1461no—
197C2×C4⋊C4—1461no—
198C2×C4⋊C4C4×D7311yescharacteristic
199C2×C4⋊C4C4×D7311yescharacteristic
200C2×C4⋊C4C22⋊D7311yescharacteristic
201C2×C42—1461no—
202C2×C42—1461no—
203C2×C42D29211yescharacteristic
204C2×C42D29211yescharacteristic
205C2×C42C22×D7311yescharacteristic
206C4⋊C8—734no—
207C4⋊C8—1462no—
208C4⋊C8—1462no—
209#101—24no—
210C22⋊C8—1462no—
211#97—22no—
212#97—1462no—
213#97—1462no—
214C4×C8—22no—
215C4×C8—1462no—
216#95—731no—
217#95—731no—
218#95—1461no—
219#95—1461no—
220#95—1461no—
221#95—1461no—
222#95—1461no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—2922no—
227C2×Q8—1462no—
228C22×C4—1461no—
229C22×C4—1461no—
230C22×C4—1461no—
231C22×C4—1461no—
232C22×C4#1192400511yescharacteristic
233C22×C4#1192400511yescharacteristic
234C22×C4#1192400511yescharacteristic
235C22×C4#1192400511yescharacteristic
236C22×C4C2×C4×D7311yescharacteristic
237C22×C4C2×C22⋊D7311yescharacteristic
238C22×C4C2×D29211yescharacteristic
239M16—24no—
240M16—42no—
241C2×C8—42no—
242C2×C8—1464no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—2922no—
247C4⋊C4—2922no—
248C4⋊C4—2922no—
249C4⋊C4—2922no—
250C4⋊C4—2922no—
251C4⋊C4—1462no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—2921no—
257C42—2921no—
258C42—1464no—
259C42D4×D7312yes—
260C42#1192402712yes—
261C23C2×#1192400511yescharacteristic
262Q8—44no—
263Q8—2922no—
264Q8—1464no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—2921no—
279C2×C4—2921no—
280C2×C4—2921no—
281C2×C4—2921no—
282C2×C4—2921no—
283C2×C4—2921no—
284C2×C4—2921no—
285C2×C4—2921no—
286C2×C4—2921no—
287C2×C4—1462no—
288C2×C4—1462no—
289C2×C4—1462no—
290C2×C4#1455651912yes—
291C2×C4#1455655112yes—
292C2×C4#1455656111yescharacteristic
293C2×C4#1455656312yes—
294C2×C4#1455657511yescharacteristic
295C8—44no—
296C8—2924no—
297C22—21no—
298C22—21no—
299C22#1798846411yescharacteristic
300C22C2×#1455651911yescharacteristic
301C22#1798860511yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—2922no—
310C4—2922no—
311C4—2922no—
312C4—5841no—
313C4#1798877212yes—
314C2—21no—
315C2—21no—
316C2#2261023111yescharacteristic
317C2#2261032211yescharacteristic
318C2#2261034711yescharacteristic
subgroupG/H
centerC2×C4#14556561
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC4×#101×C73C2
socleC22×C73#386
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenterC4×#101D73
hypocenterC73#9030
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
165. C73#9030semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226190162
#226132222
#226083792
#226078252
C4×#101×C732
#903073